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We adopt a two-moment formalism, together with a reference-metric approach, to express the equations of relativistic radiation hydrodynamics in a form that is well-suited for numerical implementations in curvilinear coordinates. We…
A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong…
We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…
We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…
In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…
Simple, self-similar, analytic solutions of 1 + 1 dimensional relativistic hydrodynamics are presented, generalizing the Hwa - Bjorken boost-invariant solution to inhomogeneous rapidity distributions. These solutions are generalized also to…
Multidimensional shock-capturing numerical schemes for special relativistic hydrodynamics (RHD) are computationally more expensive than their correspondent Euler versions, due to the nonlinear relations between conservative and primitive…
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
The importance of contact discontinuities in 2D isothermal flows has rarely been discussed, since most Riemann solvers are derived for 1D Euler equations. We present a new contact resolving approximate Riemann solver for the isothermal…
We describe a novel Godunov-type numerical method for solving the equations of resistive relativistic magnetohydrodynamics. In the proposed approach, the spatial components of both magnetic and electric fields are located at zone interfaces…
We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is firstly presented in a general 4-dimensional setting and then specialized to the case of…
We present a semi-Lagrangian characteristic mapping method for the incompressible Euler equations on a rotating sphere. The numerical method uses a spatio-temporal discretization of the inverse flow map generated by the Eulerian velocity as…
The characteristic formulation of the relativistic hydrodynamic equations (Donat et al 1998 J. Comput. Phys. 146 58), which has been implemented in many relativistic hydro-codes that make use of Godunov-type methods, has to be slightly…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…
We provide the set of equations for non-relativistic fluid dynamics on arbitrary, possibly time-dependent spaces, in general coordinates. These equations are fully covariant under either local Galilean or local Carrollian transformations,…
We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of Reconstruction-Evolution methods, a standard class of HRSC methods. We test three different…
We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show…
High resolution, non-oscillatory, central difference (NOCD) numerical schemes are introduced as alternatives to more traditional artificial viscosity (AV) and Godunov methods for solving the fully general relativistic hydrodynamics…
The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order Godunov-type schemes. In the past, building a generalized Riemann problem solver was seen as…